The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics

D. Demir

P. Singha Deo, Kanchan Meena

V. Gasparian, Thomas Christen, M. Büttiker

The response of an arbitrary scattering problem to quasistatic perturbations in the scattering potential is naturally expressed in terms of a set of local partial densities of states and a set of sensitivities each associated with one element of the scattering matrix. We define the local partial densities of states and the sensitivities in terms of functional derivatives of the scattering matrix and discuss their relation to the Green's function. Certain combinations of the local partial densities of states represent the injectivity of a scattering channel into the system and the emissivity into a scattering channel. It is shown that the injectivities and emissivities are simply related to the absolute square of the scattering wave function. We discuss also the connection of the partial densities of states and the sensitivities to characteristic times. We apply these concepts to a \ensuremath{\delta} barrier and to the local Larmor clock. \textcopyright{} 1996 The American Physical Society.

M. V. Feigel’man, V. V. Ryazanov, Vladislav B. Timofeev

Kanchan Meena, Ghosh, Souvik, P. Singha Deo

In a series of recent papers we have proved rigorously that time travel is a reality and very much feasible by using quantum mechanical processes. There are plenty of indirect experimental support untill a direct experiment is conducted. The process crucially depend on the reality of a local time as well as a local partial density of states (LPDOS) that can become negative very easily in the quantum regime of mesoscopic systems. Mesoscopic systems are small enough to allow us to experimentally access the intermediate regime between the classical and quantum worlds. This LPDOS is in every sense a hidden variable in quantum mechanics that does not show up in the axiomatic framework of quantum mechanics. It can be inferred through physical clocks obeying quantum dynamics and can be rigorously justified from the properties of the Hilbert space that is uniquely isomorphic to the complex plane. Therefore one can naturally guess that LPDOS will have something important to say about quantum measurement as well as the unification of classical and quantum laws. We therefore undertake the exercise to show that LPDOS can very much allow us to re-interpret the enormously successful phenomenological Landauer-Buttiker formalism for mesoscopic systems and put it on firm theoretical ground as a bridge between classical and quantum mechanics, thereby unifying them. Essentially the local time calculated quantum mechanically can dilate exactly like the proper time of relativity and be consistent with the coordinate time of relativity. Also the measured conductance of mesoscopic samples is a deterministic quantum measurement outcome from a linear superposition of states, essentially because of LPDOS, which solves the quantum measurement problem. For this we analyze the three probe conductance formula in details and give our arguments for the general case.

H. M. Krenzlin, Jan Budczies, K. W. Kehr

The Larmor clock which was proposed to determine tunneling times of particles with spin through barriers is studied. Tunneling of wave packets is numerically derived from the time-dependent Schr\"odinger-Pauli equation. The Larmor clock often does not proceed unidirectionally in time. The asymptotic readings are well defined. For wide wave packets the asymptotic Larmor times agree with the stationary-state predictions; deviations are seen for narrow wave packets. B\"uttiker's dwell time is investigated and its connection with the Larmor times is confirmed in the case of wave packets. \textcopyright{} 1996 The American Physical Society.